Henri Poincaré Quotes

Later generations will regard Mengenlehre (set theory) as a disease from which one has recovered.

Having reached Coutances, we entered an omnibus to go some place or other. At the moment when I put my foot on the step the idea came to me, without anything in my former thoughts seeming to have paved the way for it, that the transformations I had used to define the Fuchsian functions were identical with those of non-Euclidean geometry. I did not verify the idea; I should not have had time, as, upon taking my seat in the omnibus, I went on with a conversation already commenced, btu I felt a perfect certainty. On my return to Caen, for conscience's sake I verified the result at my leisure.

only reach him after having traversed reflecting media of complicated form. The two indications which serve us in judging distances would cease to be connected by a constant relation. A being who should achieve in such a world the education of his senses would no doubt attribute four dimensions to complete visual space.

Correlative movement' therefore constitutes the sole connection between two phenomena which otherwise we never should have dreamt of likening.

It's through science that we prove, but through intuition that we discover.

El hombre de ciencia no estudia la naturaleza porque sea útil; la estudia porque encuentra placer, y encuentra placer porque es bella. Si la naturaleza no fuera bella, no valdría la pena conocerla, ni valdría la pena vivir la vida. No hablo aquí, entendámoslo bien, de esta belleza que impresiona los sentidos, de la belleza de las cualidades y de las apariencias; no es que la desdeñe, lejos de ahí, pero no tiene nada que ver con la ciencia. Quiero hablar de esa belleza, más íntima, que proviene del orden armonioso de las partes y que sólo una inteligencia pura puede comprender. Por así decirlo es ella la que da un cuerpo, un esqueleto a las halagadoras apariencias que embellecen nuestros sentidos, y sin este soporte, la belleza de estos sueños fugitivos sería imperfecta, porque sería indecisa y huiría siempre

In reality, space is therefore amorphous, a flaccid form, without rigidity, which is adaptable to everything, it has no properties of its own. To geometrize is to study the properties of our instruments, that is, of solid bodies.

A demonstration really based upon the principles of Analytical Logic will be composed of a succession of propositions ; some, which will serve as premises, will be identities or definitions ; others will be deduced from the former step by step ; but although the connexion between each proposition and the succeeding proposition can be grasped immediately, it is not obvious at a glance how it has been possible to pass from the first to the last, which we may be tempted to look upon as a new truth. But if we replace successively the various expressions that are used by their definitions, and if we pursue this operation to the furthest possible limit, there will be nothing left at the end but identities, so that all will be reduced to one immense tautology. Logic therefore remains barren, unless it is fertilized by intuition.

if the contrary takes place, if these two muscular sensations vary independently of one another, we shall have to take account of one more independent variable, and 'complete visual space' will appear to us as a physical continuum of four dimensions.

O societate este cu atât mai înaintată, cu cât are mai mare grijă faţă de bufonii ei.

Only Science and Art make civilization worth-while. One may be startled by the formula: Science for the sake of Science; and yet, it is worth as much as Life for Life's sake, if life is but misery; and even as Happiness for Happiness' sake, unless one believes that all pleasures are the same in quality, unless one is ready to admit that the goal of civilization is to furnish alcohol to all who love to drink.
All actions have goals. We must suffer, we must work, we must pay for our seats at the show. But, we pay that we may see, or that, at least, others may see some day.

the sum of the angles of a triangle is equal to two right angles; but this is because the triangles we deal with are too little; the difference, according to Lobachevski, is proportional to the surface of the triangle; will it not perhaps become sensible when we shall operate on larger triangles or when our measurements shall become more precise? The Euclidean geometry would thus be only a provisional geometry.

Mathematicians are born, not made.

The very possibility of mathematical science seems an insoluble contradiction. If this science is only deductive in appearance, from whence is derived that perfect rigour which is challenged by none? If, on the contrary, all the propositions which it enunciates may be derived in order by the rules of formal logic, how is it that mathematics is not reduced to a gigantic tautology? The syllogism can teach us nothing essentially new, and if everything must spring from the principle of identity, then everything should be capable of being reduced to that principle. Are we then to admit that the enunciations of all the theorems with which so many volumes are filled, are only indirect ways of saying that A is A?

La recherche de la vérité doit être le but de notre activité ; c'est la seule fin qui soit digne d'elle. Sans doute nous devons d'abord nous efforcer de soulager les souffrances humaines, mais pourquoi ?